I can answer for this part of your question:
You are right. At the university where I am at, the database group is broken into two sections: theory and systems. Although we all work together and learn from each other, it is good to know ahead of time whether you wish to focus on theory or the systems side. I do not know much about the research trends for the theory in databases, but I know that working with big data analytics, cloud computing, data visualization, data integration, are popular areas in the field. It helps to also go to conference specifically in the area. When I went to SIGMOD back in May, you can easily tell what the 'big areas' are based on the publications and posters.
And yes, not every school has a database research group. Make sure you look into that before applying (if you are focusing on databases).
Hope this helps a bit